Example 2
Which of the following list of numbers does form an AP? If they form an AP, write the next two terms :
4, 10, 16, 22
Difference between 2nd and 1st term
= 10 4
= 6
Difference between third and second term
= 16 10
= 6
Difference between fourth and third term
= 22 16
= 6
Since difference is same, it is an AP
Common difference = d = 6
We have to find next two terms
We are given 4 terms .
So, we have to find 5th and 6th terms .
5th term = 4th term + common difference
= 22 + 6
= 28
6th term = 5th term + common difference
= 28 + 6
= 34
Hence 5th and 6th terms are 28 and 34.
Example 2
Which of the following list of numbers does form an AP? If they form an AP, write the next two terms :
(ii) 1, 1, 3, 5, .
Difference between 2nd and 1st term = ( 1) (1)
= 1 1
= 2
Difference between 3rd and 2nd term = 3 ( 1)
= 3 + 1
= 2
Difference between 4th and 3rd term = ( 5) ( 3)
= 5 + 3
= 2
Since difference is same, it is an AP
Common difference = d = 2
We have to find next two terms
We are given 4 terms .
So, we have to find 5th and 6th terms .
5th term = 4th term + common difference
= 5 + ( 2)
= 5 2
= 7
6th term = 5th term + common difference
= 7 + ( 2)
= 7 2
= 9
Hence the 5th and 6th term of the series are 7 and 9.
Example 2
Which of the following list of numbers does form an AP? If they form an AP, write the next two terms :
(iii) 2, 2, 2, 2, 2, .
Difference between 2nd and 1st term
= 2 ( 2)
= 2 + 2
= 4
Difference between 3rd and 2nd term
= 2 (2)
= 2 2
= 4
Since, difference is not same .
4 4
Hence it is not an AP
Example 2
Which of the following list of numbers does form an AP? If they form an AP, write the next two terms :
(iv) 1, 1, 1, 2, 2, 2, 3, 3, 3,
Difference between 2nd and 1st terms = 1 1
= 0
Difference between 3rd and 2nd terms = 1 1
= 0
Difference between 4th and 3rd term = 2 1
= 1
Since difference is not same
0 1
Hence it is not an AP.